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Some effectivity questions for plane Cremona transformations in the context of symmetric key cryptography

Part of: Birational geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  01 March 2021

N. I. Shepherd-Barron
N. I. Shepherd-Barron*
Affiliation:
Department of Mathematics, King's College London, Strand, LondonWC2R 2LS, UK (nicholas.shepherd-barron@kcl.ac.uk)
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Abstract

An effective lower bound on the entropy of some explicit quadratic plane Cremona transformations is given. The motivation is that such transformations (Hénon maps, or Feistel ciphers) are used in symmetric key cryptography. Moreover, a hyperbolic plane Cremona transformation g is rigid, in the sense of [5], and under further explicit conditions some power of g is tight.

MSC classification

Primary: 14E07: Birational automorphisms, Cremona group and generalizations
Secondary: 14G50: Applications to coding theory and cryptography
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 1 , February 2021 , pp. 1 - 28
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Copyright
Copyright © The Authors, 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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